Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator

TL;DR

This paper demonstrates that a dynamically disordered quantum walk can generate maximal entanglement between a qubit’s internal and external degrees of freedom, outperforming ordered walks and applicable in experimental tests.

Contribution

It introduces a model of disordered quantum walks that achieves asymptotic maximal entanglement regardless of initial states, with practical experimental proposals.

Findings

Maximal entanglement is achieved asymptotically in disordered QRW.

Disorder enhances entanglement compared to ordered QRW.

Maximal entanglement is independent of initial states.

Abstract

We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system's time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.